Applications of Kato’s inequality for n-tuples of operators in Hilbert spaces, (I)

By the use of the celebrated Kato's inequality we obtain in this paper some inequalities for operator-valued integrals on a complex Hilbert space H. Among others, we show that [Formula: see text] for any x, y ∈ H, provided [Formula: see text] and p : E → [0, ∞) are μ-measurable functions on E and such that [Formula: see text] and [Formula: see text] are Bochner integrable on E for some α ∈ [0, 1]. Natural applications for various norms and numerical radii associated with the Bochner integral of operator-valued functions and some examples for the operator exponential are presented as well.

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Gaussian Hilbert Spaces

10.1017/cbo9780511526169 ◽

1997 ◽

Cited By ~ 257

Author(s):

Svante Janson

Keyword(s):

Hilbert Spaces

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On split equality monotone Yosida variational inclusion and fixed point problems for countable infinite families of certain nonlinear mappings in Hilbert spaces

Novi Sad Journal of Mathematics ◽

10.30755/nsjom.10119 ◽

2020 ◽

Vol Accepted ◽

Author(s):

Oluwatosin Temitope Mewomo ◽

Hammed Anuoluwapo Abass ◽

Chinedu Izuchukwu ◽

Olawale Kazeem Oyewole

Keyword(s):

Fixed Point ◽

Hilbert Spaces ◽

Fixed Point Problems ◽

Variational Inclusion ◽

Nonlinear Mappings

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Analytic and Sequential Feynman Integrals on Abstract Wiener and Hilbert Spaces, and A Cameron-Martin Formula. Revision.

10.21236/ada146969 ◽

1984 ◽

Author(s):

G. Kallianpur ◽

D. Kannan ◽

R. L. Karandikar

Keyword(s):

Hilbert Spaces ◽

Feynman Integrals

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Unbounded Linear Operators

10.1093/oso/9780198812050.003.0003 ◽

2018 ◽

Author(s):

D. E. Edmunds ◽

W. D. Evans

Keyword(s):

Hilbert Spaces ◽

Linear Operators ◽

Von Neumann ◽

Limit Circle ◽

Sectorial Operators ◽

Closed Operators ◽

The Stability ◽

Symmetric Operators ◽

Unbounded Linear Operators ◽

Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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